This paper proposes the coordinated control of a hybrid AC/DC power system with renewable energy source, energy storages and critical loads. The hybrid microgrid consists of both AC and DC sides. A synchronous generator and a PV farm supply power to the system's AC and DC sides, respectively. A bidirectional fully controlled AC/DC converter with active and reactive power decoupling technique is used to link the AC bus with the DC bus while regulating the system voltage and frequency. A DC/DC boost converter with a maximum power point tracking (MPPT) function is implemented to maximize the energy generation from the PV farm. Current controlled bidirectional DC/DC converters are applied to connect each lithium-ion battery bank to the DC bus. Lithium-ion battery banks act as energy storage devices that serve to increase the system stability by absorbing or injecting power to the grid as ancillary services. The proposed system can function in both grid-connected mode and islanding mode. Power electronic converters with different control strategies are analyzed in both modes in detail. Simulation results in MATLAB Simulink verify that the proposed topology is coordinated for power management in both AC and DC sides under critical loads with high efficiency, reliability, and robustness under both grid-connected and islanding modes.